3(y-7)(y+2)=0

Solution for 3(y-7)(y+2)=0 equation:

Simplifying
3(y + -7)(y + 2) = 0

Reorder the terms:
3(-7 + y)(y + 2) = 0

Reorder the terms:
3(-7 + y)(2 + y) = 0

Multiply (-7 + y) * (2 + y)
3(-7(2 + y) + y(2 + y)) = 0
3((2 * -7 + y * -7) + y(2 + y)) = 0
3((-14 + -7y) + y(2 + y)) = 0
3(-14 + -7y + (2 * y + y * y)) = 0
3(-14 + -7y + (2y + y2)) = 0

Combine like terms: -7y + 2y = -5y
3(-14 + -5y + y2) = 0
(-14 * 3 + -5y * 3 + y2 * 3) = 0
(-42 + -15y + 3y2) = 0

Solving
-42 + -15y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -5y + y2) = 0

Factor a trinomial.
3((-2 + -1y)(7 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve:

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-2, 7}